| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Oliveira, Roberto, I, IMPA, BR-22460320 Rio De Janeiro - Brazil
[2] Univ Calif San Diego, Dept Mech & Aerosp Engn, San Diego, CA 92093 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | ELECTRONIC JOURNAL OF PROBABILITY; v. 25, 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by Erdos-Renyi graphs with constant mean degree. The limiting object is related to a potentially infinite system of SDEs defined over a Galton-Watson tree. Our theorems apply more generally, when the sequence of graphs ({''}decorated{''} with edge and vertex parameters) converges in the local weak sense. Our main technical result is a locality estimate bounding the influence of far-away diffusions on one another. We also numerically explore the emergence of synchronization phenomena on Galton-Watson random trees, observing rich phase transitions from synchronized to desynchronized activity among nodes at different distances from the root. (AU) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |